This paper presents for the first time a solution to the Problem of decentralized adaptive asymptotic tracking for a new class of large-scale systems using nonlinear output feedback. The proposed constructive approach does not require any matching conditions on the parametric uncertainties nor growth conditions of any kind on the subsystem and interacting output nonlinearities. Any decentralized system in the family may have an unknown, nonzero equilibrium point. Partially decentralized reduced-order filters are presented to recover the unmeasured states. The recursive, decentralized, output-feedback design procedure is illustrated in a practical example of two inverted pendulums on carts without velocity measurements. The effectiveness of the decentralized algorithm is supported by simulation results.